integral of sqrt(x)-(x-2)

Lösung

\int x - (x - 2) d x

\frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + 2 x + C

Schritte zur Lösung

\int x - (x - 2) d x

Vereinfache

= \int x - x + 2 d x

Wende die Summenregel an:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int x d x - \int x d x + \int 2 d x

\int x d x = \frac{2}{3} x^{\frac{3}{2}}

\int x d x = \frac{x ^{2}}{2}

\int 2 d x = 2 x

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + 2 x

Füge eine Konstante zur Lösung hinzu

= \frac{2}{3} x^{\frac{3}{2}} - \frac{x ^{2}}{2} + 2 x + C

d er i v a t i v e ln (w)

\frac{d}{d t} (a cos (t) + t^{2} sin (t))

d er i v a t i v e g (t) = 3 t + 5 t + 9

(2 x + 8 y) d x + (8 x + 4 y) d y = 0

d er i v a t i v e f (x) = \frac{x}{x ^{2} - 5}